Problem: Simplify the following expression: $ p = \dfrac{6}{x - 9} + \dfrac{8}{3} $
In order to add expressions, they must have a common denominator. Multiply the first expression by $\dfrac{3}{3}$ $ \dfrac{6}{x - 9} \times \dfrac{3}{3} = \dfrac{18}{3x - 27} $ Multiply the second expression by $\dfrac{x - 9}{x - 9}$ $ \dfrac{8}{3} \times \dfrac{x - 9}{x - 9} = \dfrac{8x - 72}{3x - 27} $ Therefore $ p = \dfrac{18}{3x - 27} + \dfrac{8x - 72}{3x - 27} $ Now the expressions have the same denominator we can simply add the numerators: $p = \dfrac{18 + 8x - 72}{3x - 27} $ $p = \dfrac{8x - 54}{3x - 27}$